Why do loudspeakers need cabinets, anyway?﻿

In junior-high physics, I was very impressed by the wave-theory experiment in which a cotton swab beat a steady rhythm on the surface of the water and created concentric circles. When they reached a wide gate, they continued in an arc, and when they reached a narrow gate they turned into straight lines. Air behaves identically, if less visibly, when it is set in motion by our loudspeakers. Sound is dispersed in a spherical shape as long as the membrane width is small in relation to the wavelength. If the loudspeaker is free-standing, it creates an “acoustic short-circuit”; the air compressed by the speaker creates a pressure vacuum behind it, so a listener standing further than a wavelength away hears almost nothing. If we want to hear lower notes, we have to increase the width of the membrane. The formula we will use later, “wavelength L equals sound speed c in the air (approx. 340 m per second) divided by frequency f,” or L= c / f (1) in meters, at about 34 Hertz, produces a somewhat unwieldy value for the membrane size in practice. There is another way: if you use an infinite baffle board to separate the front and back sides of the membrane, the air can do its best, but it won’t be able to equalize the pressure. It’s hard to find an infinite baffle board, not to mention that you would need two for a stereo – and I hate to think of equipping a home theater. If you were willing to give up the lower frequencies, it would also work to mount the speaker in an appropriate-sized hole in the outer wall of your apartment and close all of the windows tightly whenever you listen to music – but I wouldn’t want to be standing outside when six neighbors decided to do the same thing at once. Fortunately, there are other ways to compromise! ﻿

A closed cabinet!﻿

In 1898, English physicist Oliver Lodge used electricity to coax soft tones out of a device with a fixed coil and a movable iron core – that was the start of the inexorable victory march of the electrodynamic loudspeaker, without which today’s information society would be unthinkable. The introduction of public radio on 10/29/1923 created a general need for sound converters that could make radio waves audible to the ears of entire families. After 1925, when Western Electric engineers Wente and Turas invented the predecessor of nearly every currently used loudspeaker, clever minds focused on developing more and more new concepts to support bass reproduction by the object of their desire. This resulted in tubes, transmission lines and other constructs, sometimes with extremely complicated deflections designed to effectively transport the sound from the back of the membrane around to the living room. Only the closed box dispensed with the necessary effort of putting together hundreds of internal dividers, false floors and sound conductors – but unfortunately it didn’t leave much room for the living area, either. The goal of the closed speaker box was to prevent the “acoustic short-circuit” between the front and back sides of the membrane. In place of the “infinite baffle board,” which could not be realized with good reason, the developers built a cabinet so big that it didn’t impede the speaker’s transmission behavior. The rigid membrane suspension was responsible for damping the natural resonance, along with the electromagnet that powered the voice coil. Because of the low efficiency factor of speakers in those days, the “infinite baffle” model only gained popularity after World War II, since by then (thanks to military research) strong fixed magnets made of “rare-earth metals” were available, with high performance due to the push-pull pentode amplifier. Nonetheless, the speaker boxes were still unacceptably large for living-room use, so the good old table-top radio and its successors remained the most common way for people to listen to music at home. The constant presence of music at home – although now it’s hard to imagine life without it – only became possible in 1954, when Edgar Villchur and Henry Kloss presented a closed loudspeaker with “acoustic suspension”: the Acoustic Research AR-1. They drew on a 1949 patent by Harry Olsen (RCA/Victor) that had broken completely new ground in chassis construction with a soft membrane suspension and a deep natural resonance. Finally, the long road to the living room opened up with the AR 2A shelf speaker, and later with the famous AR-3, which contained a 12-inch long-throw bass in addition to the soft-dome-calotte tweeters and mid-range speakers. That opened the door to enjoying music at home on the couch, because finally the speaker boxes left some space for the rest of the family to be in the room, too. When the boxes were also made shallower, people found they could even hide them behind curtains to protect them from the eyes of curious neighbors – so the (naturally) white LS 730 Braun boxes were among those classic representatives of the species that were often heard but rarely seen. The closed box was replaced in the consumers’ affections in the early ’70s by the bass reflex boxes, which were based on a wealth of scientific findings and solid theory; their inventors Neville Thiele and Richard Small, apart from all their contributions, were also responsible for the years that potential box buyers spent chasing down salespeople with the question, “Do you have a three-path one with 150 watts and a bass reflex?”

Closed box structures were out of style for some time, but for several years they have been experiencing a renaissance, especially in the areas of high-quality home theater and auto subwoofers. But even in the field of do-it-yourself speaker construction, more and more people are considering the advantages. To keep these kinds of speakers from “chattering” long after the record (or, nowadays, the CD or DVD) has been put back on the shelf, they are built into a very small compact box whose volume is somewhere between one-third and one-tenth of the Vas equivalent volume of the chassis. Their reset force comes mainly from the spring rigidity of the air cushion enclosed in the box. The cabinet installation increases the resonance of the bass in terms of the Qtc to Qts ratio, and deep bass dispersion is possible even with a small cabinet if the natural resonance is deep enough. Since closed boxes also act as second-order deep-pass filters (the sound-pressure decay below the installed resonance is 12 rather than the usual 24 dB/octave for open constructions), we hear even lower bass ranges than from other boxes, at a perceptible volume. The lower efficiency factor compared to open boxes is no longer significant with today’s amplifiers, and in exchange we get a “clean” bass with more details and contour because we don’t have to rely on bass amplification by dispersing sound from the back side of the membrane. Within the limits allowed by the speaker, we can influence the bass replay characteristics through the cabinet size: smaller box, higher Qtc and vice versa. Qtc values around 1.0 tend to have a warmer, more powerful bass reproduction, while Qtcs smaller than 0.8 have better dynamics and sound more detailed, but restrained. The best transient behavior is guaranteed by a Qtc of 0.5 – but in exchange for the dynamic perfection, you have to accept a -3 dB frequency that is a couple of Hertz higher. The insulation filling is important for the sound of closed boxes. The sound dispersed from the back of the membrane cannot be allowed to permeate back out through the membrane, so it needs to be largely destroyed in the cabinet. This is done by firmly pressed, fibrous materials like mineral wool, which rubs against the air molecules carrying the sound and transforms the sound energy into heat, thereby rendering it harmless. Foams like Prittex are useless here. We have also had good experiences with soft fiberboard, which can be glued to the interior walls to combat the cabinet vibrations. For larger cabinets, reinforcement rings placed at irregular intervals should be a given. Since no air can come out of any part of the box, all of the interior gluing should also be sealed off with acrylic sealing compound or our famous assembly glue, and the speakers should be closed off with sealing tape. Another application that should not be overlooked for the closed box, one that has been in use “forever,” is in the mid-range. Here it not only decouples sound from the bass, but also applies filter characteristics as a significant tuning method – in some cases, a smaller chamber can provide the missing “body,” and a larger one can create richer piano impulses.﻿

Horns﻿

When you talk to other people about horns, you always run up against the perception that horns sound tinny or too loud, and the most common complaint is that they sound like megaphones. If you ask them how they know this, it usually turns out that they weren’t listening to horns themselves, but rather to other people who told them about it and repeated it often enough that they started to believe it was their own experience and thus the truth. If you tell them the perception might not be accurate, they always say there’s no need for those dinosaurs of the loudspeaker world in today’s era of “dollar-a-watt” amplifiers; after all, their training bikes have long since been replaced by cars, too. Since time immemorial, people have taken it for granted that anything shaped more or less like a funnel can amplify sound in a purely mechanical way. So they built musical instruments that could signal the approach of the ruler from far away, or simply to draw people’s attention. They are even described as wall-breaking weapons of war in one of our oldest texts (when the besieged city of Jericho couldn’t be accessed in the usual way, troops armed with trumpets or horns marched around it three times, at which the city walls crumbled and allowed the city to be taken over). After the invention of the gramophone, horns were added to these devices as well – soon, sounds reminiscent of voices and instruments could be heard emanating from the funnel. Using the triode tube designed by Lee DeForest, with a structure similar to today’s headphones, it became possible to coax out a higher volume than ever before. However, this did not mark the end, but rather the start of “horn amplification” in loudspeaker construction. In order to avoid having to wear headphones while listening to the radio, developers used the gramophone’s funnel principle for sound amplification and achieved a reproduction quality that was unheard-of for the time (our pampered high-end ears would complain about it, but in another 100 years people may be laughing themselves sick over our ‘achievements’ in the world of sound). The groundbreaking discovery came from Bell engineers Wente and Thuras in 1928, with their patent for a loudspeaker with a pressurized chamber, a free-standing voice coil and an inverse aluminum membrane. Western Electric, a company belonging to Bell, took over its commercial implementation and set standards with early models like the 555/555W, which is still one of the best according to today’s standards (unfortunately they are almost impossible for us to hear nowadays, since a reputable source tells me that 99% of them are now being enjoyed by Japanese audiophiles). Except for the permanent magnet – which is standard today but was still too expensive at the time – and the design of the phase plug, these mid-ranges and tweeters combined with a corresponding horn have not seen any significant changes. Without them, the movie-theater organist’s job would still exist; but along with the desire to hear more natural-sounding human voices, Hollywood’s desire to bring moviegoers closer to their favorite actors also increased (even if this seems to have stopped more than one career dead in its tracks). And so began the triumphant march of the “talkie,” with 1927’s important epic “The Jazz Singer,” featuring the popular Al Jolson singing for the first time in a movie. It was closely accompanied by the further development of truly loud speakers, since it was now necessary to reach the back row of a large audience with good enough quality that people could understand the dialogue (the front was the “razor seat”). In order to play back music that included the bass range, the “front-loaded” pressurized-chamber loudspeaker was no longer enough; new concepts were needed. English inventor P.G.A.H. Voigt, with his “rear-loaded” bass and full-range horns, running on drivers with very lightweight paper membranes, was a pioneer in this area. As in the early days, they are still manufactured by the Lowther company. Unfortunately, there’s no room in this article to talk in more detail about the structure of the Tractrix horn that he generally used in his designs. Just after the end of World War II, however, the horn’s days were numbered. With the invention of the “push-pull” pentode, which offered much higher performance, and especially with the transistor amplifier and its almost unlimited power, developers were able to cut down the coffin-sized boxes – with the direct sound transducers launched by Rice and Kellogg, even the growing hunger for wattage couldn’t prevent them from coaxing big volume out of handy little boxes. Curiously enough, a few sticks in the mud managed to miss this development – so, despite all advice to the contrary, there is still a small band of horn enthusiasts on the music consumer scene who stubbornly refuse to acknowledge the musical superiority of small two-path “high-end” boxes. They doggedly insist that the horns’ greater efficiency is not their only advantage. What else could there be to distinguish them? Well, let’s take a closer look at how a horn “works” before we jump onto any of the common bandwagons. Our investigation will be limited to the abovementioned “rear-loaded” exponential bass horns, although there are plenty of analogies with all of the other horn formats. Precisely speaking, a horn loudspeaker consists of 5 connected components: the speaker, the pressure chamber, the horn throat, the horn length and the horn mouth. So what does each component do? The speaker performs the work. The goal is a high efficiency factor, which is achieved with a lightweight membrane, ideally an underhung voice coil (avoids the weight of a long wrap) and a high force factor of B x 1. The membrane affects the pressure chamber. This is a calculable space behind the speaker whose outlet opening A is smaller than the membrane surface M (in the literature, various calculation approaches are mentioned, some based on approximation formulas and some on Thiele/Small parameters, both for the chamber and for the opening. However, these are not significant for describing the two processes, so we will not use any formulas here). The movement of the membrane presses a certain volume of air through the narrower outlet opening, which increases the flow velocity of the air according to the ratio M/A. Along with the higher radiation resistance and the increased efficiency factor, this dampens the deflection of the membrane, which creates reduced distortions. It might be tempting at this point to increase the efficiency factor by designing smaller and smaller outlet openings, but there is a natural limit. If the opening is too narrow, it creates air vortices, which in turn make themselves known through increased distortion or a rushing sound; or, with an even smaller outlet, the air no longer passes through and the desired effects break off prematurely. The velocity transformation created at the outlet declines at higher frequencies, since air can be compressed. In other words, the radiation resistance lessens and the efficiency factor drops. As a rule of thumb, the larger the pressure chamber, the sooner the volume drops off at higher frequencies. This creates an upper frequency limit for the effects of the pressure chamber, in which the horn’s sound transmission is gradually taken over by the speaker membrane. Together, the speaker and pressure chamber form a new driver with improved sound dispersion conditions due to the horn that starts behind it – the course of the horn’s opening from the throat to the mouth can be conical, exponential, hyperbolic or parabolic. The lowest frequency dispersed by the horn determines the mouth area for the funnel. It becomes larger (until it is no longer manageable) according to how low the box is meant to play. If you put the horn on the floor (which is common for bass horns), the mouth opening is cut in half, since the sound is now only dispersed into the room in a hemispherical shape. It is halved again if you put the speaker in front of a wall, and the horn mouth is at its smallest when the speaker is set up in the corner of a room. That makes the size of the box a little more living-room friendly. Once the sizes of the horn’s mouth and throat are determined, the horn length can be determined using the geometry of the course and the associated “funnel constants.” The funnel constant determines the relationship of the horn’s opening to its length. It is linear for cones, and in all other cases the opening is based on the corresponding parabolic, exponential and hyperbolic functions. The horn throat and mouth are the same size in every model. The small opening against the membrane surface produces high pressure at the horn throat with low particle acceleration, which is transformed into low pressure and high particle acceleration due to the expanding area in the course of the horn. The real job of the funnel is adapting the radiation resistance of the (relatively) small loudspeaker to the surrounding room, thereby increasing the acoustic performance – at the mouth of the horn, the radiation resistance of the sound source is adapted to the resistance in the ambient air. The curve of the sound-pressure decrease toward the lower frequency limit is also determined by the horn’s geometry; the pressure declines most quickly in a conical course, which results in a flatter decline. In a hyperbolic course, the pressure declines more slowly, which also increases distortion. The expo horn presents a good compromise between the two. As sound pressure increases, the effect of sound focusing due to reflections in the horn course should also be taken into account. But how could the features described here make horn boxes superior to direct sound transducers? Improved energy conversion means that a “horn-loaded” membrane needs less lift for the same volume than a direct transducer of the same size. However, since the distortions created by the speaker depend on the lift, they are smaller in the first instance than the second. At the same volume, the horn-driven loudspeaker leaves the amplifier with larger reserves to represent the impulse peaks, since it reaches its deflection limits much later (or, due to the neighbors’ complaints, not at all). The same sound pressure can be created by a smaller membrane with a smaller mass, which improves the impulse reproduction; transient and decay processes are more effortless. This creates a more lively, prompt and less effortful reproduction of dynamic musical passages such as drum solos, industrial bands like Einstürzende Neubauten and harpists gone wild (Deborah Henson-Conant: Just for You: “Under The Bed.” Highly recommended!). In short, a horn speaker is more dynamic and produces much less distortion, with improved impulse responses and less amplifier stress. That’s why the true fan associates the term “horn sound” with the adjectives clear, dynamic, physical, present and detailed, but in all honesty it also means the unapologetic and “most brutal disclosure” of every fault in the transmission chain, in the recordings being played and even in the acoustics of the room. Naturally, the construction of a horn has more to do with care than speed. It would also be unreasonable to ignore the living-room aspect when it comes to looking at horns. Many outstanding horn constructions are still slumbering in the heads of enthusiastic horn designers because there’s no room to set up the finished product. Besides, the argument “if you loved me, you’d let me crank up my speakers in this room!” can lead to an undesirable, if understandable outcome: plenty of space in the room … without you in it.﻿

Transmission lines﻿

It’s the year 2000 A.D. The entire world of speaker construction is ruled by legions of simulation programs that allow you to precisely predict the sound pressure and phasing in every room and for every possible model, down to the dB, without needing us to reach for the wood and the glue to build a test cabinet … The entire world? Not exactly!! Surrounded by armies of calculable bass reflex boxes, there is still a small band of steadfast horns, brave transmission lines and open baffle boards that have so far been able to resist all attempts to force them into a satisfactory electro-acoustic model. In this issue and the ones to come, K&T will be dedicating the attention to them that they rightfully deserve, due to the endless possibilities and constant challenges that they offer construction-happy developers. What better place than our universally beloved “Cheap trick” column to present these unusual assembly suggestions? Just to be clear, I don’t have anything against simulation programs – after all, they make a speaker developer’s calculations many times easier than we could ever have imagined. Once the parameters have been entered (based on measurements, if possible), they give me a rough idea of the expected results of my work; however, if a letter-writer expresses doubts about the accuracy of our measurements for a subwoofer because all 4 (four) of the sim. progs calculated different frequency responses, I would suggest coming to terms with the fact that sim. progs don’t represent reality. As their name indicates, they just want us to believe what they tell us. Unfortunately for them and fortunately for us, the reality is much more complex, so it cannot be explained by a handful of parameters – otherwise loudspeaker builders would have to get a real job, and hobbyists would have to start looking for a new hobby…

The open tube If I separate the front and back sides of the membrane with a tube that is open in back, the acoustic short-circuit shifts to lower frequencies according to the tube length, since the sound has to travel farther in order to equalize the pressure. If the speaker is moved at a certain frequency, first it swings forward and pushes the surrounding air in its path; at the same time, it draws in air from the back side. This suction effect reaches the end of the tube after a delay. The speaker’s largest deflection takes place after a quarter of the time needed to complete a full vibration. Now, it is moving backward half of the time. Ideally, this should coincide with the arrival of the suction effect at the end of the tube. This is the case if the tube length is exactly one-fourth of the wavelength of the initial frequency. Another useful effect: at the maximum membrane deflection, a pressure wave counteracts the movement, since the air in front of the speaker and at the tube outlet is moving in the same manner as the air behind the membrane, but in the opposite direction. The lowest frequency at which a speaker can produce sound (with conventional stimulus) is its natural resonance, indicated by a clear increase in the impedance level. At this frequency, the speaker is set strongly in motion by a small amount of energy; in other words, its power rating is low and requires as much damping as possible. As described above, we choose a tube length that is one-fourth the wavelength of the loudspeaker’s resonance. We calculate the tube length using the following formula: L = / 4 (2) in meters If we insert c / f into (1), we get: L = c / (4 x f) in meters where c = sound velocity in the air (approx. 340 m/sec ) and f = resonant frequency. In order to get an idea of the dimensions for a running line, let’s calculate them at a resonance of 34 Hertz (Hz), just for fun: L = 340 / (4 x 34) = 340 / 136 = 2.50 m I haven’t said anything about the diameter of the open tube yet. Assuming that the sound in the tube has to cover the same distance, at the same amplitude, as it does outside the tube, its cross-section for the entire length must correspond to the membrane diameter. In the available literature (which unfortunately is very limited), you can also find recommendations for using a line that tapers, starting at 1.25 to 2 times the membrane diameter and decreasing to 0.9 to 0.7 times the diameter. Another common model prefers a pre-chamber with a connected line, calculated using the formulas for closed cabinets. This model is reminiscent of a bass reflex cabinet with a very long reflex channel. Hobbyists who enjoy experimenting can find plenty of room in all these approaches for their own practical tests. This box type is closely linked with the “trial and error” approach, given that even its current name – the “transmission line” – goes back to an error on the part of its developer, A. R. Bailey. In his initial attempt, Bailey had actually hoped to find a running line that would destroy the sound that was diffused backward. Since few people would voluntarily dig two 2.5-meter tunnels in their homes, it makes sense to bend the channel as often as possible, creating a still-large but more convenient size. Of course, the bends cause reflections in the line, which are shown as small, narrow-banded impedance peaks. It should also be mentioned that the ideal damping for the speaker resonance has the opposite effect at its even-numbered multiples,which creates a wave formation in both the frequency and the impedance response. In addition, no speaker is considerate enough to limit the sound from the back to just the low notes – it also fills up the tube with frequencies well into the mid-range.

Damping the transmission line Even if Bailey made a mistake in the construction, we have him to thank for the discovery that suitable insulators can effectively prevent not only undesirable resonances and reflections but also the permeation of the mid-range notes to the end of the tube. Even the wave formation in the impedance response can be smoothed out this way, without any negative influence on the frequency response. Just the opposite – the deflection of the air molecules by the insulation material creates a slower rate of flow for air inside the channel, which leads to a 15-20% reduction in tube length. That means we can add a correction to the length formula (2): L = c x 0.8 / (4 x f) (3) Thus the running line in our 34-Hz example can be reduced to 2.00 meters, in other words a smaller box – which makes our better halves happier, too. Where and how much insulation needs to be used can be determined through measurements or listening tests. (This is where the critics always start complaining that transmission lines don’t work anyway because they can’t be calculated, and because our listening method is completely unscientific. All I have to say to those experts is that one should only reject things that one has studied in detail and that have already been proven untenable in experiments.) In my experience, an even, loose layer of insulation along the entire line, down to the last bend – polyester wool or preferably non-glued cotton polishing wool – provides the best results. Many older publications recommend sheep’s wool, which over time tends to adhere to the floor and clog up the bends in the tube. In the worst case, it negates the effect of the line; on the other hand, it gives people with an interest in biology a wonderful chance to research the breeding habits of the common clothes moth. More important than the number of bends is the placement of the channel end of the transmission line; here, too, we can create some changes in the bass behavior. The bass is reinforced near the floor and when it is near a wall, while the outlet at the top of the box is useful for weakening the bass. If the channel comes out on the back side, it can cause setup problems in smaller rooms; too much distance from the bass speaker causes interference and thus very uneven bass reproduction at various points in the room. During my four years of working at K+T, I’ve learned a few things about the ideal positioning of the bass chassis along the line. Starting with the CT 188, a large number of transmission-line boxes have been added to the loudspeaker market, with basses built in at one-third of the running length. With two basses per box, the second one was at one-fifth of the line length, which almost completely eliminated the wave formation for playing back lower frequencies. Since then, transmission lines have once again become desirable projects for hobby builders with a love of experimentation; they have even become established in home theaters, with the CT 197 and CT 206 as the main box and the CT 190 and CT 196 as corner towers or wall-hung speakers.

Which speaker is the correct one? In principle, the above considerations apply to any speaker, but I think loudspeakers with a Qts between 0.4 and 0.6, and with as deep a natural resonance as possible, are ideal. Because of their parameters, they allow for sufficiently loud and contoured bass deflection. A higher Qts leads to a worsened impulse response, which is why I tend to recommend a different box type here. If the Qts is low, the speaker also has a relatively high resonance and its sound pressure drops off too sharply at lower frequencies. Still, once again the phrase holds true: don’t pass along any experiences that you haven’t had yourself – after all: It’s the year 2000 A.D. …

Tonal advantages I wouldn’t tell anyone to build speaker boxes according to the above principles if they were just looking for a bass with a “boom” or a “roar.” The strengths of this model come from its quiet intermediate tones; the cabinet resonances are almost completely suppressed, and the impedance response is fairly flat, which also makes a transmission-line speaker an interesting companion for tube amplifiers; the sound pressure is even all the way down to the resonant frequency of the loudspeaker. Since no cavity resonances are created in the cabinet, the relatively thin membrane also does not emit any reflected sounds from the inside that would add to the music signal. As a result, the transmission line plays almost without any discoloration up to the middle of the bass range (above that, the sound deflection through the membrane takes over). Of course that doesn’t mean a transmission line can’t be loud. Because it doesn’t have to work against an enclosed air cushion, it lacks the annoyance of the compression when the membrane is thrown back by the spring rigidity of the interior air as if on a trampoline, even though it hasn’t reached the necessary lift to create the sound pressure (here, too, the other speakers are also responsible for any unsatisfactory results). A speaker construction principle that gets by with so few formulas and rules gives box-builders more creative freedom than any other project, but I can guarantee one thing: every transmission line works. Some are better and some are worse, but the results are never boring, because you haven’t worked everything out in a simulation in advance.

Band-pass cabinet﻿If you look at the construction drawing for a band-pass cabinet, it’s not hard to understand the theory by Armin Jost, inventor of the “AJHorn” simulation program, that all speaker-box models are just variations on horns. Clearly, the inventor of this assembly seems to have forgotten about the funnel outlet, or else he designed it to be very short and straight. On the other hand, it’s not wrong to describe band-passes as closed cabinets with an acoustic filter at the front; but however we look at them, their unusual position among the other cabinet models comes from only allowing an internal integrated chassis with a small frequency range of sound dispersion. As a result, they are exclusively used for subwoofer constructions ranging up to 150 Hz. Contrary to popular belief, the history of the band-pass did not start in 1979 with KEF developer Laurie Fincham and his AES article “A Bandpass Loudspeaker Enclosure”; rather, the first patent was registered in 1934 by the Frenchman Andre D'Alton, followed by Henry Lang in 1952. At the time, though, there was no commercial interest in using the principle. Only in 1982, when design engineers Augris and Santens published a pocket-calculator calculation for it in the French journal “L’Audiophil,” did the band-pass become usable. It had its commercial heyday with a design patented by Bose in 1965, with two-sided ventilated chambers, in the three-piece Acoustimass speaker system. In 1988, it became accessible for amateur builders when the Augris/Santens method was republished by Jean Margerand in “Speaker Builder,” soon followed by the first assembly kits in the Fidibus and Intus series by Dr. Manfred Hubert. The introduction of the computer to the construction process and the associated calculation speed means that now there are countless different models, some with cascading, nested reflex chambers that no human being could ever understand. For instance, the “Bassyst 2” sim. prog sold by Adam Hall calculates an assembly in which the two-sided ventilated band-pass works with a reflex chamber positioned in front of it.﻿

closed/reflex ventilated on both sides reflex/reflex vent. on both sides/reflex

Our analysis will be limited to the traditional closed/reflex band-pass format, though there is a certain (but not calculable) similarity to the other formats. In a band-pass system, the speaker is always inside the box. The back side plays on a closed volume Vr, and the front plays on a reflex chamber Vf. This system, coordinated via a reflex channel, acts like a second-order filter on both sides of the transmission band (hence the name). Its limits are established by the lower (F1) and upper (F2) -3 dB frequency, and are symmetrically positioned in relation to the middle frequency F0 on the logarithmic frequency scale. The bandwidth is determined by the damping factor S (a dimensionless value between 0 and 1); the smaller S is, the wider the band, the more rippled the frequency response and the lower the efficiency factor. Ripple refers to the volume difference between F1, F2 and F0; for S = 0.7, it is 0 dB, while for S = 0.5 there is a (theoretical) increase of 1.25 dB in F1 and F2, which also means the best impulse response where S = 0.7. For any given driver, the three construction variables – the front volume (Vf), the rear volume (Vr) and the middle frequency of the band-pass (F0) – determine the transmission behavior of the cabinet. The front volume depends on the chassis parameters and the damping factor S. It is calculated as follows: Vf = (2 x S x Qts)⊃2; x Vas [1] where Qts = free-standing value and Vas = equivalent volume of the chassis. The rear volume determines the frequency response and efficiency factor of the system. The calculation is the same as for closed boxes: Vr = Vas / ((Qtc / Qts)⊃2; - 1) [2] where Qtc = installed value of the chassis and is larger than Qts. The middle frequency of the band-pass corresponds to the installed resonance of the chassis in the closed chamber, and is determined using F0 = Qtc x (Fs/Qts) [3] where Fs = free-standing resonance of the chassis. The last value to be determined is the tuning frequency for the bass reflex chamber, and thus the length of the reflex tube. The system is in tune when the Helmholz resonant frequency (in relation to Vf) and the middle frequency are the same. This creates the following, based on the familiar formula for the reflex tube length: L = 94248 x r⊃2; / (Vf x F0⊃2;) - 1,6 x r where L = length and r = radius of the reflex tube. (94248 comes from rounding up the meter factors 3 x 10000 x , 1.6 from 0.9 x , which is the correct formula, but harder to type into a calculator accurately) In order to change the transmission behavior of the band-pass, we have the following options:

1. Changing the damping factor S By reducing the size of the reflex cabinet, the smaller S gives us a wider frequency band with the same middle frequency, a lower efficiency factor and worsened impulse response, while an increase does the opposite. However, since the front volume increases proportionally as the square of S, improving the impulse response unfortunately requires a much bigger box. ﻿

2. Changing the installed Q, Qtc﻿Enlarging the closed cabinet produces a deeper adjustment with a lower efficiency factor, and does not change the ripple or the bandwidth. Even though the diagrams are trying to tell us that the bandwidth decreases as Qtc increases, it remains at about 50 Hz for all of them, while with the upper diagrams it declines significantly – from about 90 Hz to 30 Hz.

In the early days of band-pass technology, because of the 12 dB filter effect at high frequencies, it was often recommended to leave out frequency crossovers in order to produce a lower Qtc. Unfortunately, the resonance of the reflex tube shows obvious, sound-disrupting peaks between about 500 and 900 Hz and at their multiples. These tunnel resonances can only be limited by active or passive filters; the latter require a recalculation for the box unless you have already taken the ohm resistance of the coils into account and included it in the crossover. The radius of the reflex tube should be as large as possible in order to avoid rushing noises, and it should not end directly under or over the bass chassis.

Today, band-pass subwoofers are almost obsolete, since amplifiers with DSP-controlled bass management are almost the rule. In addition, because they only reveal their good impulse responses in a fairly large cabinet, they are losing their attractiveness in the age of miniaturization. In addition, there is plenty of amplifier performance available, so even watt-hungry closed boxes with an additional deep-bass distortion offer more than enough volume. Still, band-passes have a chance of surviving as integrated subwoofers if they are combined with a small two-way system; here they can act as a stand as well as an invisible bass support. With the right speakers, this composition can have a pleasant side effect: resolving the age-old battle of the sexes between cabinet size (generally female) and bass power (generally male), once and for all. In this context, the interested reader is strongly advised to take a look at the FirstTime 10 and 12 models. With their invisible chassis in the band-pass as well as a visible bass mid-range speaker, they offer a huge amount of listening pleasure with the smallest possible dimensions﻿